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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSun, 19 Dec 2010 12:48:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t12927627856c99m24ejfomps5.htm/, Retrieved Sun, 05 May 2024 02:18:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112333, Retrieved Sun, 05 May 2024 02:18:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [paperuit_ACF2] [2010-12-19 12:48:24] [13dfa60174f50d862e8699db2153bfc5] [Current]
-   P     [(Partial) Autocorrelation Function] [paperuit_ACF2] [2010-12-19 14:09:42] [7e261c986c934df955dd3ac53e9d45c6]
-   P       [(Partial) Autocorrelation Function] [ACFbis_uitvoerbelgie] [2010-12-22 14:38:38] [8441f95c4a5787a301bc621ebc7904ca]
-             [(Partial) Autocorrelation Function] [Kristof Nagels] [2010-12-24 15:04:14] [8441f95c4a5787a301bc621ebc7904ca]
-   P       [(Partial) Autocorrelation Function] [paperACF_uit2] [2010-12-24 14:26:30] [74be16979710d4c4e7c6647856088456]
-             [(Partial) Autocorrelation Function] [Kristof Nagels] [2010-12-24 15:05:06] [8441f95c4a5787a301bc621ebc7904ca]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15
14.4
13
13.7
13.6
15.2
12.9
14
14.1
13.2
11.3
13.3
14.4
13.3
11.6
13.2
13.1
14.6
14
14.3
13.8
13.7
11
14.4
15.6
13.7
12.6
13.2
13.3
14.3
14
13.4
13.9
13.7
10.5
14.5
15
13.5
13.5
13.2
13.8
16.2
14.7
13.9
16
14.4
12.3
15.9
15.9
15.5
15.1
14.5
15.1
17.4
16.2
15.6
17.2
14.9
13.8
17.5
16.2
17.5
16.6
16.2
16.6
19.6
15.9
18
18.3
16.3
14.9
18.2
18.4
18.5
16
17.4
17.2
19.6
17.2
18.3
19.3
18.1
16.2
18.4
20.5
19
16.5
18.7
19
19.2
20.5
19.3
20.6
20.1
16.1
20.4
19.7
15.6
14.4
13.7
14.1
15
14.2
13.6
15.4
14.8
12.5
16.2
16.1
16
15.8
15.2
15.7
18.9
17.4
17
19.8
17.7
16
19.6
19.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112333&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112333&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112333&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.361462-3.54160.000308
20.0802420.78620.216841
30.3306513.23970.000822
4-0.22105-2.16580.0164
50.1563891.53230.06437
60.1284131.25820.105689
7-0.311554-3.05260.001467
80.1685461.65140.050962
9-0.070596-0.69170.245397
10-0.137396-1.34620.090703
110.0040060.03920.484387
12-0.218225-2.13820.017521
130.0123570.12110.451943
140.0162180.15890.43704
15-0.024038-0.23550.407151
16-0.16704-1.63660.052489
170.1132481.10960.134972
180.0033890.03320.486789
19-0.087323-0.85560.197178
200.0869460.85190.198198

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.361462 & -3.5416 & 0.000308 \tabularnewline
2 & 0.080242 & 0.7862 & 0.216841 \tabularnewline
3 & 0.330651 & 3.2397 & 0.000822 \tabularnewline
4 & -0.22105 & -2.1658 & 0.0164 \tabularnewline
5 & 0.156389 & 1.5323 & 0.06437 \tabularnewline
6 & 0.128413 & 1.2582 & 0.105689 \tabularnewline
7 & -0.311554 & -3.0526 & 0.001467 \tabularnewline
8 & 0.168546 & 1.6514 & 0.050962 \tabularnewline
9 & -0.070596 & -0.6917 & 0.245397 \tabularnewline
10 & -0.137396 & -1.3462 & 0.090703 \tabularnewline
11 & 0.004006 & 0.0392 & 0.484387 \tabularnewline
12 & -0.218225 & -2.1382 & 0.017521 \tabularnewline
13 & 0.012357 & 0.1211 & 0.451943 \tabularnewline
14 & 0.016218 & 0.1589 & 0.43704 \tabularnewline
15 & -0.024038 & -0.2355 & 0.407151 \tabularnewline
16 & -0.16704 & -1.6366 & 0.052489 \tabularnewline
17 & 0.113248 & 1.1096 & 0.134972 \tabularnewline
18 & 0.003389 & 0.0332 & 0.486789 \tabularnewline
19 & -0.087323 & -0.8556 & 0.197178 \tabularnewline
20 & 0.086946 & 0.8519 & 0.198198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112333&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.361462[/C][C]-3.5416[/C][C]0.000308[/C][/ROW]
[ROW][C]2[/C][C]0.080242[/C][C]0.7862[/C][C]0.216841[/C][/ROW]
[ROW][C]3[/C][C]0.330651[/C][C]3.2397[/C][C]0.000822[/C][/ROW]
[ROW][C]4[/C][C]-0.22105[/C][C]-2.1658[/C][C]0.0164[/C][/ROW]
[ROW][C]5[/C][C]0.156389[/C][C]1.5323[/C][C]0.06437[/C][/ROW]
[ROW][C]6[/C][C]0.128413[/C][C]1.2582[/C][C]0.105689[/C][/ROW]
[ROW][C]7[/C][C]-0.311554[/C][C]-3.0526[/C][C]0.001467[/C][/ROW]
[ROW][C]8[/C][C]0.168546[/C][C]1.6514[/C][C]0.050962[/C][/ROW]
[ROW][C]9[/C][C]-0.070596[/C][C]-0.6917[/C][C]0.245397[/C][/ROW]
[ROW][C]10[/C][C]-0.137396[/C][C]-1.3462[/C][C]0.090703[/C][/ROW]
[ROW][C]11[/C][C]0.004006[/C][C]0.0392[/C][C]0.484387[/C][/ROW]
[ROW][C]12[/C][C]-0.218225[/C][C]-2.1382[/C][C]0.017521[/C][/ROW]
[ROW][C]13[/C][C]0.012357[/C][C]0.1211[/C][C]0.451943[/C][/ROW]
[ROW][C]14[/C][C]0.016218[/C][C]0.1589[/C][C]0.43704[/C][/ROW]
[ROW][C]15[/C][C]-0.024038[/C][C]-0.2355[/C][C]0.407151[/C][/ROW]
[ROW][C]16[/C][C]-0.16704[/C][C]-1.6366[/C][C]0.052489[/C][/ROW]
[ROW][C]17[/C][C]0.113248[/C][C]1.1096[/C][C]0.134972[/C][/ROW]
[ROW][C]18[/C][C]0.003389[/C][C]0.0332[/C][C]0.486789[/C][/ROW]
[ROW][C]19[/C][C]-0.087323[/C][C]-0.8556[/C][C]0.197178[/C][/ROW]
[ROW][C]20[/C][C]0.086946[/C][C]0.8519[/C][C]0.198198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112333&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112333&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.361462-3.54160.000308
20.0802420.78620.216841
30.3306513.23970.000822
4-0.22105-2.16580.0164
50.1563891.53230.06437
60.1284131.25820.105689
7-0.311554-3.05260.001467
80.1685461.65140.050962
9-0.070596-0.69170.245397
10-0.137396-1.34620.090703
110.0040060.03920.484387
12-0.218225-2.13820.017521
130.0123570.12110.451943
140.0162180.15890.43704
15-0.024038-0.23550.407151
16-0.16704-1.63660.052489
170.1132481.10960.134972
180.0033890.03320.486789
19-0.087323-0.85560.197178
200.0869460.85190.198198






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.361462-3.54160.000308
2-0.057989-0.56820.28562
30.3928533.84920.000107
40.044310.43410.332579
50.0370670.36320.358633
60.1073721.0520.147715
7-0.245128-2.40180.009121
8-0.150453-1.47410.071859
9-0.087162-0.8540.197614
10-0.014874-0.14570.442217
11-0.137044-1.34270.09126
12-0.259606-2.54360.006284
13-0.043056-0.42190.337036
140.0830540.81380.208898
150.2589122.53680.006399
16-0.154479-1.51360.066709
17-0.051296-0.50260.3082
180.0485410.47560.317718
19-0.107954-1.05770.146416
20-0.111832-1.09570.137971

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.361462 & -3.5416 & 0.000308 \tabularnewline
2 & -0.057989 & -0.5682 & 0.28562 \tabularnewline
3 & 0.392853 & 3.8492 & 0.000107 \tabularnewline
4 & 0.04431 & 0.4341 & 0.332579 \tabularnewline
5 & 0.037067 & 0.3632 & 0.358633 \tabularnewline
6 & 0.107372 & 1.052 & 0.147715 \tabularnewline
7 & -0.245128 & -2.4018 & 0.009121 \tabularnewline
8 & -0.150453 & -1.4741 & 0.071859 \tabularnewline
9 & -0.087162 & -0.854 & 0.197614 \tabularnewline
10 & -0.014874 & -0.1457 & 0.442217 \tabularnewline
11 & -0.137044 & -1.3427 & 0.09126 \tabularnewline
12 & -0.259606 & -2.5436 & 0.006284 \tabularnewline
13 & -0.043056 & -0.4219 & 0.337036 \tabularnewline
14 & 0.083054 & 0.8138 & 0.208898 \tabularnewline
15 & 0.258912 & 2.5368 & 0.006399 \tabularnewline
16 & -0.154479 & -1.5136 & 0.066709 \tabularnewline
17 & -0.051296 & -0.5026 & 0.3082 \tabularnewline
18 & 0.048541 & 0.4756 & 0.317718 \tabularnewline
19 & -0.107954 & -1.0577 & 0.146416 \tabularnewline
20 & -0.111832 & -1.0957 & 0.137971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112333&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.361462[/C][C]-3.5416[/C][C]0.000308[/C][/ROW]
[ROW][C]2[/C][C]-0.057989[/C][C]-0.5682[/C][C]0.28562[/C][/ROW]
[ROW][C]3[/C][C]0.392853[/C][C]3.8492[/C][C]0.000107[/C][/ROW]
[ROW][C]4[/C][C]0.04431[/C][C]0.4341[/C][C]0.332579[/C][/ROW]
[ROW][C]5[/C][C]0.037067[/C][C]0.3632[/C][C]0.358633[/C][/ROW]
[ROW][C]6[/C][C]0.107372[/C][C]1.052[/C][C]0.147715[/C][/ROW]
[ROW][C]7[/C][C]-0.245128[/C][C]-2.4018[/C][C]0.009121[/C][/ROW]
[ROW][C]8[/C][C]-0.150453[/C][C]-1.4741[/C][C]0.071859[/C][/ROW]
[ROW][C]9[/C][C]-0.087162[/C][C]-0.854[/C][C]0.197614[/C][/ROW]
[ROW][C]10[/C][C]-0.014874[/C][C]-0.1457[/C][C]0.442217[/C][/ROW]
[ROW][C]11[/C][C]-0.137044[/C][C]-1.3427[/C][C]0.09126[/C][/ROW]
[ROW][C]12[/C][C]-0.259606[/C][C]-2.5436[/C][C]0.006284[/C][/ROW]
[ROW][C]13[/C][C]-0.043056[/C][C]-0.4219[/C][C]0.337036[/C][/ROW]
[ROW][C]14[/C][C]0.083054[/C][C]0.8138[/C][C]0.208898[/C][/ROW]
[ROW][C]15[/C][C]0.258912[/C][C]2.5368[/C][C]0.006399[/C][/ROW]
[ROW][C]16[/C][C]-0.154479[/C][C]-1.5136[/C][C]0.066709[/C][/ROW]
[ROW][C]17[/C][C]-0.051296[/C][C]-0.5026[/C][C]0.3082[/C][/ROW]
[ROW][C]18[/C][C]0.048541[/C][C]0.4756[/C][C]0.317718[/C][/ROW]
[ROW][C]19[/C][C]-0.107954[/C][C]-1.0577[/C][C]0.146416[/C][/ROW]
[ROW][C]20[/C][C]-0.111832[/C][C]-1.0957[/C][C]0.137971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112333&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112333&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.361462-3.54160.000308
2-0.057989-0.56820.28562
30.3928533.84920.000107
40.044310.43410.332579
50.0370670.36320.358633
60.1073721.0520.147715
7-0.245128-2.40180.009121
8-0.150453-1.47410.071859
9-0.087162-0.8540.197614
10-0.014874-0.14570.442217
11-0.137044-1.34270.09126
12-0.259606-2.54360.006284
13-0.043056-0.42190.337036
140.0830540.81380.208898
150.2589122.53680.006399
16-0.154479-1.51360.066709
17-0.051296-0.50260.3082
180.0485410.47560.317718
19-0.107954-1.05770.146416
20-0.111832-1.09570.137971


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = -0.6 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = -0.6 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')